Metamath Proof Explorer


Theorem r19.3rzvOLD

Description: Obsolete version of r19.3rzv as of 16-Feb-2026. (Contributed by NM, 10-Mar-1997) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion r19.3rzvOLD ⊢ A ≠ ∅ → φ ↔ ∀ x ∈ A φ

Proof

Step Hyp Ref Expression
1 nfv ⊢ Ⅎ x φ
2 1 r19.3rz ⊢ A ≠ ∅ → φ ↔ ∀ x ∈ A φ